Scanning TEM (STEM): Imaging & Resolution Duncan Alexander! EPFL-CIME Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 1 Contents • • • • • • • • • Principles of STEM (optics, design, reciprocity theorem)! Convergence and collection angles! Bright-field (BF) and annular dark-field (ADF) imaging! High angle annular dark-field (HAADF)/z-contrast imaging! Spatial resolution in STEM, the electron probe! The electron Ronchigram! Aberration correction in STEM! New imaging modes (MAADF, ABF, SE)! Limitations, references Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 2 Principles of STEM Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 3 e--matter interactions • With STEM we can use many more of these signals in a highly spatiallyresolved way than we can with TEM! • Furthermore we can record different signals in parallel, have an improved Backscattered electrons BSE Auger electrons “absorbed” electrons secondary electrons SE Characteristic X-rays Specimen direct beam 1-100 nm Incident beam ultimate resolution and more easily interpretable atomic resolution images incoherent elastically scattered electrons coherent elastically scattered electrons Duncan Alexander: STEM Imaging & Resolution visible light electron-hole pairs Bremsstrahlung X-rays inelastically scattered electrons CIME, EPFL 4 Principle of STEM • • • Electromagnetic lens focuses electrons from FEG on to sample! Beam deflectors scan beam across sample! For each probe position (x, y) record signal intensity I(x, y) and/or spectrum! • • Display/record image(s) of I(x, y)! Integrated signal from hyperspectral datasets (e.g. 3D datacube axes x, y, E) Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 5 Optics of TEM vs STEM • TEM: fixed beam, broad “parallel” illumination, objective lens that forms image after the specimen. Image projected onto camera! • Scanning TEM: lens forms focused probe on sample, scanned across sample in raster pattern. For each probe position (x, y) detect a signal intensity (or spectrum), convert to (x, y) image. Quiz: what type of diffraction pattern will one see in STEM mode? Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 6 Convergent beam electron diffraction Because STEM uses a focused – i.e. converged – e– beam, scattering in the sample gives a convergent beam electron diffraction pattern Figures by Jean-Paul Morniroli Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 7 Dedicated STEM design • VG STEMs (1970s–1990s) and Nion UltraSTEMs (now) made “upside down” with the electron gun at the bottom! • Original STEMs had no lenses after samples; just detectors measuring integrated signal at different scattering angles, and energy-loss in transmitted electrons (EELS). Conceptually this still applies today.! • The properties of the probe-forming lens determine the image and its resolution – i.e. it is the image-forming lens. Therefore in the STEM community it is referred to as the “objective lens” and its aperture as the “objective aperture”. Be careful with terminology, especially since on a combined TEM/STEM it is still the “condenser lens”!! • Often refer to fixed beam TEM as CTEM (conventional TEM)! • After sample detect only scattering angles – like far-field diffraction with no subsequent TEM image plane Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 8 Dedicated STEM design Early VG STEM Duncan Alexander: STEM Imaging & Resolution Nion UltraSTEM 200 (www.nion.com) CIME, EPFL 9 Dedicated STEM design Varela et al. Annu. Rev. Mater. Res. 2005 35 539–69 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 10 TEM/STEM design • Many modern field emission gun TEMs can also be used as STEMS (e.g. JEOL 2200FS, FEI Tecnai Osiris in CIME)! • STEM detectors are inserted in the back focal plane of the objective lens! • Use nano-beam (highly convergent) illumination – mini-condenser lens off! • • Scan beam with TEM beam shift coils! Modern TEMs STEM detectors send signal to computer acquisition software Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 11 TEM/STEM design Ray diagrams:! TEM mode! ! ! STEM mode CM strongly excited => parallel beam CM de-excited => converged beam Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 12 STEM imaging detectors Focused e- probe scanned on sample; disc and annular detectors in back focal (diffraction) plane EDX spectrometer Scan beam Semi-conductor detector: X-rays EELS spectrometer High-angle annular dark-field => compositional contrast: intensity ∝ t Z2 (thickness t, atomic number Z) Scintillator photomultiplier (PMT) detector: Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 13 STEM detectors and signals • With STEM we have the possibility to sample many different signals on different detectors, and can acquire that data with high spatial precision (atomic – nm scale)! • Therefore we can probe many different aspects of a sample; its structure, chemistry and physics! • For instance in CIME we have access to the following STEM detectors:! • Bright-field; Annular bright-field; Annular dark-field; High angle annular dark-field (z-contrast); Secondary electron; Backscattered electron; Energy-dispersive X-ray (EDX) spectrometer; Electron energy-loss spectrometer (EELS); CCD camera; cathodoluminescence spectrometer! • Often we can acquire multiple signals in parallel, e.g. JEOL 2200FS: HAADF, EELS, CL Osiris: HAADF, DF4, DF2, BF/image + EDX spectrum! • This adds significantly to the capabilities of STEM Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 14 Reciprocity Theorem for equivalence of TEM and STEM bright-field imaging Recprocity Theorem (from geometric optics): The amplitude of a wave a B due to an electron source at A is equal to the amplitude at A’ due to a source at B’. J.M. Cowley Applied Physics Letters 15 (1969) 58 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 15 Convergence and collection angles • • • • The focused probe is a convergent electron beam. The BF and DF detectors are radially symmetric. Therefore all of them are characterised by angles – angle of convergence for the beam; collection of scattering angles for the detectors! ! The convergence semi-angle of the probe is called !! A collection semi-angle for a detector is called β! Knowledge of these angles is important for STEM imaging βBF βDF, outer βDF, inner Quiz: for reciprocity with BF CTEM with a perfectly parallel incident beam, what collection angle do we need for the BF detector in STEM? Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 16 Bright-field & Annular dark-field detectors • BF detector is a solid disc, dark-field detectors are ring shaped – i.e. annular – with certain inner and outer collection semi-angles β! • If the inner β is set-up to collect only diffracted beams we obtain a diffraction contrast darkfield image! • Diffraction Diffraction intensity is an integration over all the selected beams – like an integration of multiple CTEM DF images Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 17 Diffraction contrast from BF & ADF signals • As crystal tilts relative to incident beam/ changes thickness, the diffraction condition changes! • Defects also change diffraction condition! • Theses changes will change integrated signal on BF (red) and ADF (blue) detectors, and so change image intensity => diffraction contrast images Si [1 0 0] 1° tilt from Si [1 0 0] 2° tilt from Si [1 0 0] Si [2 2 5] Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 18 Bright-field STEM imaging example • • Polycrystalline ZnO thin-film on glass substrate! Image rather equivalent to that from BF TEM, but bit more “averaging” of grain contrast Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 19 DF TEM vs ADF STEM imaging • Photovoltaic stack (polycrystalline ZnO/proto-Si/polycrystalline-Si/ZnO) DF TEM image: strong contrast, few grains have intensity ADF STEM image: more grains have intensity, so more grain visibility & less contrast Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 20 ADF STEM imaging example • Photovoltaic stack (polycrystalline ZnO/proto-Si/polycrystalline-Si/ZnO) Visible: protocrystalline/crystalline Si interface, B-doped layer in proto-Si, voids Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 21 Influence of convergence angle • Increasing convergence semi-angle α (e.g. by using larger condenser aperture) => diffraction discs overlap more! • Interference between discs can lead to phase contrast image Si [1 0 0] Si [1 0 0] Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 22 Influence of collection angle • Increasing collection semi-angle β (e.g. by reducing camera length) => include diffracted beams on BF detector (integrated BF and DF intensity); ADF detector collects higher angle scattered beams Si [1 0 0] Si [1 0 0] Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 23 Bright-field/annular dark-field detectors! – Influence of camera length Big camera length small camera length ADF BF Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 24 High-resolution BF STEM imaging • Following from the theory of reciprocity, with a sufficiently small probe a BF detector can produce an image equivalent to a HR-TEM image.! • • This is conditional on having CBED discs overlapping on the BF detector.! No overlap is like BF CTEM imaging with only the direct beam chosen, so will give no fringes Figure from Pennycook & Nellist “Scanning Transmission Electron Microscopy” Quiz: for a particular lattice spacing, how can we change convergence semi-angle ! to have more disc overlap? Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 25 Fringes from annular dark-field • The ADF detector can have overlapped fringes when the BF detector does not! • This will result in fringes in the ADF image even if there are none in the BF image! • Still assumes there is coherent elastic scattering; what happens if we increase collection angle β? Figure from Pennycook & Nellist “Scanning Transmission Electron Microscopy” Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 26 High angle annular dark-field (HAADF) imaging Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 27 Rutherford scattering • Coulombic interaction with the electron cloud → low angle scattering! • Coulombic interaction with the nucleus → higherangle scattering! • Rutherford cross-section for high-angle scattering by nucleus alone:! ! • Including screening and relativistic correction:! ! ! • When scattering angle > screening parameter θ0 the electron nucleus interaction is dominant (E0 is in keV); e.g. Cu, 200 keV beam θ0 ≈ 25 mrad Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 28 High-angle annular dark field (HAADF) • • • By using a detector/ camera length combination that gives large collection angles (e.g. β >80–100 mead) we can more or less collect the Rutherfordscattered exclusively! HAADF Big camera length These angles are typically too large for coherent elastic scattering (i.e. diffraction)! small camera length ADF BF This is called high-angle annular dark-field (HAADF) Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 29 HAADF/Z-contrast imaging • By collecting only Rutherfordscattered electrons, the HAADF detector produces an image which (ideally) gives an intensity: I tZ2 ∝ for thickness t, average atomic number Z! • Diffraction contrast is eliminated (or at least much reduced…)! • In reality: I tZ1.6–2 ∝ Figure from Pennycook “Scanning transmission electron microscopy : imaging and analysis” Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 30 HAADF/Z-contrast imaging Z-contrast examples: Pt catalyst on Al2O3 Duncan Alexander: STEM Imaging & Resolution Si-Ge/Si multilayer CIME, EPFL 31 HAADF/Z-contrast imaging Z-contrast examples: Figure from Pennycook “Scanning transmission electron microscopy : imaging and analysis” Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 32 HAADF/Z-contrast imaging Z-contrast examples: Figure from Pennycook “Scanning transmission electron microscopy : imaging and analysis” Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 33 Coherent vs Incoherent imaging • In the 1970s, biologists Engel et al. and Misell et al. proved that the integration of signals on an ADF detector represents a convolution of intensities instead of amplitudes: ! ! • The fundamental equation for incoherent images is therefore obtained: ! ! • Compared to coherent – i.e. phase contrast – imaging, incoherent imaging has some specific (useful!) characteristics:! ‣ No image contrast inversion with defocus! ‣ “Camera-like characteristics”! ‣ Broad optical transfer function Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 34 Optical transfer function of incoherent imaging • • Incoherent imaging gives a better spatial resolution than coherent imaging! This was proved by Lord Rayleigh in 1896 (Phil. Mag. 42, p. 167); the Rayleigh criterion for resolution basically applies “Scanning Transmission Electron Microscopy”, P.D. Nellist, in Science of Microscopy Vol. 1, Springer 2007 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 35 Spatial resolution of incoherent imaging • The above results mean that an ADF STEM image has a fundamentally improved spatial resolution compared to its BF counterpart! • Only realised on materials science samples once HAADF detector introduced since the lower-angle ADF detector collects too much coherent diffraction signal to achieve incoherency! • In contrast Rutherford-scattered electrons are fundamentally incoherent; this scattering destroys the phase relationship Figure from Pennycook “Scanning transmission electron microscopy : imaging and analysis” Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 36 The electron source and probe • To benefit from these advantages of STEM we need a very well focused electron probe! • • • This requires: good optics and a small source! • Cold field emission gun has smaller source, higher brightness than warm, Schottky field emission gun; becoming popular again (Nion, JEOL ARM, Hitachi) Why do we need a small source?! A field emission gun is mandatory: Albert Crewe (and VG) used cold field emission guns! Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 37 The electron source and probe Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 38 The electron Ronchigram Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 39 The Electron Ronchigram as we see it • • • STEM mode; fix the probe; large/no aperture in probe-forming lens! Record 2-D image of intensity in diffraction (i.e. STEM detector) plane! See “shadow image” of sample in the diffraction disc Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 40 Basics of shadow image formation Assuming perfect optics At overfocus the STEM detector plane is a shadow image of the sample Magnification M = dprobe-detector/dprobe-sample At underfocus the image will be magnified, but also inverted Ronchigram is similar to defocused TEM diffraction pattern, blending image information with scattering angles Diagram from: “Scanning Transmission Electron Microscopy”, P.D. Nellist, in Science of Microscopy Vol. 1, Springer 2007 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 41 Shadow image formation in the presence of large spherical aberration J.M. Cowley Ultramicroscopy 4 (1979) 413 Gaussian focus G; paraxial magnification M = R1/R0 J.M. Cowley Ultramicroscopy 4 (1979) 435 Underfocus: infinite magnification for rays that cross at S Gaussian and overfocus: magnification decreases smoothly for larger angles Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 42 Radii and azimuths of infinite magnification Radii Azimuths • • • The underfocus Ronchigram shows infinite magnification at more than one scattering angle! In fact there are radii (radial spokes) and tangential azimuths (rings) of infinite magnification! Why is this? Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 43 Radii and azimuths of infinite magnification Phase shift due to aberration in Front Focal Plane of “objective” lens (TEM = “condenser”): From this, Cowley derived that: In 1-D: M: magnification for Cs = 0; M’: actual magnification ‒ consistent with overfocus image, however infinite magnification would only occur at: However in 2-D derivation there are two critical angles: Radial magnification is infinite for: Circumferential magnification is infinite for: J.M. Cowley Journal of Electron Microscopy Technique 3 (1986) 25 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 44 So why is it called the “Ronchigram”? While not referred to as the Electron Ronchigram in Cowley’s first papers describing the phenomena, by 1986 this term was used by analogy to the optical tests for aberrations developed by Vasco Ronchi [1-3] V. Ronchi Applied Optics 3 (1964) 437 If we are rigorous Electron Ronchigram only refers to scattering from periodic objects; however the term is used more generally for the figure from amorphous phase too [1] Ultramicroscopy 4 (1979) 413; [2] Ultramicroscopy 4 (1979) 435; [3] Journal of Electron Microscopy Technique 3 (1986) 25 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 45 Aligning STEM mode with the Ronchigram Correcting astigmatism: characteristic “American football” when astigmatic Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 46 Focusing with the Ronchigram From criterion that phase shift must not depart more than π/4 from 0, it is found that for a given Cs of “objective” lens optimal defocus is: Allowing “objective” aperture with radius of: At optimum defocus and with correct aperture size, the probe FWHM is given by: “Scanning Transmission Electron Microscopy”, P.D. Nellist, in Science of Microscopy Vol. 1, Springer 2007 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 47 Focusing with the Ronchigram • In practice:! ‣ Reduce under-focus until infinite-magnification rings are of minimum diameter => optimum defocus (c.f. Scherzer defocus in HR-TEM)! ! Optimum probe-forming aperture diameter ! ! ! ! ‒700 nm ! ! ‣ ‒450 nm ‒250 nm Fit probe-forming aperture to the “sweet spot” region of constant phase within this diameter Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 48 Increasing probe-forming aperture size • • What happens if we increase probe-forming aperture beyond the sweet-spot?! • The sweet-spot gives a peak in the middle which does not change much; in contrast the tails go up enormously from putting in these aberrations => more signal but not from where we want Look at streak images of the electron probe from Osiris going from α ≈ 11 mrad (left) to α ≈ 16 mrad (right)! Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 49 Cs-Aberration correction in STEM • • First STEM aberration corrector installed on VG by Nion (Krivanek); quadrupoleoctopole design. This is now used on Nion UltraSTEM. CEOS aberration corrector also used for aberration-corrected STEM on many instruments (FEI, JEOL, Hitachi) Duncan Alexander: STEM Imaging & Resolution CIME, EPFL Krivanek et al. Aberration Correction in Electron Microscopy, Handbook of Charged Particle Physics 2009, pp. 601–641 50 Effect of aberration-correction on sweet spot • At optimum defocus aberration correction produces a sweet spot (region of flat phase) with much greater diameter; c.f. effect of Cs-correction on CTF in HR-TEM! • E.g. for HT 100 kV, Cs 1.0 mm, sweet spot has: With no correction αmax = 11.6 mrad With CS/C5 (as shown) correction αmax = 40 mrad ! ! • Demagnification of virtual source size by the objective (probe-forming) lens increases in proportion with illumination angle (assuming this does not exceed sweet spot diameter) => Probe size decreases as αmax–1! • Using larger probe-forming aperture also improves resolution slightly because diffraction limit reduced! • Quiz: as probe-forming aperture increased, what happens to: a) beam current? b) focal depth? Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 51 Aberration-corrected examples Z-contrast image: “direct” interpretation, but light O columns not visible. Varela et al. Annu. Rev. Mater. Res. 2005 35 539–569 BF detector gives simultaneous phase contrast image equivalent to HR-TEM image; O columns visible but similar problems to interpret as HR-TEM image Pennycook “Scanning Transmission Electron Microscopy” Chapter 1 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 52 HAADF imaging theory • Until now have taken assumption of Rutherford scattering and incoherent imaging theory to understand the HAADF Z-contrast image; this is in fact an approximation! • • What really happens: transmission of Bloch states down atomic columns! • Being peaked near nucleus the 1s Bloch state is also most highly absorbed Bloch state. For heavier columns it is almost depleted after as little as 10 nm. The remainder of crystal adds little extra intensity.! • In thicker regions when probe between columns it spreads onto neighbouring columns, giving rather uniform background intensity in image.! • • Thick sample thus “behaves” like thin sample => thickness insensitivity!! • Multi-slice image simulations using frozen phonon model; atom effectively static as e– passes on its trajectory, integrate over different vibrational atom positions 1s Bloch state dominates; this has a high intensity very close to nuclei where highangle Rutherford scattering occurs, unlike 2s or there Bloch states that peak inbetween atomic columns! Inelastic thermal diffuse scattering from phonon vibrations => jiggle of atoms that makes their scattering incoherent! Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 53 “New” imaging modes Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 54 Medium-angle ADF (MAADF) • Analysis of monolayer materials: low kV essential to prevent knock-on damage; here 60 kV used (knock-on threshold for bulk grapheme ~86 kV)! • As " increases aberration correction even more important for obtaining atomic resolution! • Medium-angle ADF gives intensity I Z1.7 but with increased signal intensity compared to true HAADF image,; this intensity is needed for imaging single atom by single atom (here β = 58–200 mrad) ∝ Krivanek et al Nature 464 (2010) 571 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 55 Annular bright-field (ABF) imaging • HAADF not useful for imaging light atoms in a sample with heavy atoms because contrast so strongly dependent on atomic number! • BF imaging has same disadvantages for imaging light atom columns as phase-contrast HR-TEM imaging! • Annular bright-field imaging (with aberration correction), where central part of BF detector is obscured, apparently solves these problems. For instance, for α = 22 mrad, use β = 11–22 mrad.! • Simulations show the ABF detector produces an “absorption” image in which light and heavy columns are visible and interpretable over a wide thickness range. Even H columns have been imaged.! • Optimal focal range very small (like HAADF) but slightly different optimum defocus to HAADF. Findlay et al. APL 95 (2009) 191913 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 56 Atomic resolution SE imaging • Zhu et al. showed atomic resolution secondaryelectron imaging from Hitachi STEM equipped with SE detector in 2009 (Nat. Mater. 8 808–812)! • Understanding of signal generation not very clear Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 57 Limitations of STEM; references • • • STEM (especially aberration-corrected) is powerful technique, but need:! • • • Sample and stage stability, resistance to beam! Electronic stability in power supplies (no scan drift and/or distortion)! Minimum possible sample contamination! These requirements are arguably more stringent than for TEM because of time needed to record a scan, and different type of beam dose and beam contamination (contamination mostly forms around the edge of a beam)! References:! • Stephen Pennycook “Scanning transmission electron microscopy : imaging and analysis” – on-line for EPFL! • P. D. Nellist “Scanning Transmission Electron Microscopy”, in Science of Microscopy Vol. 1 (ed. Stephen Hawkes) Springer 2007 Duncan Alexander: STEM Imaging & Resolution CIME, EPFL 58
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